In variable stroke axial piston machines employing a variable angle swash plate mechanism such as the automotive refrigerant compressor disclosed in U.S. Pat. 4,428,718, the reciprocating pistons induce a rotating couple on the swash plate. And if the stroke is variable as it is in the afore-mentioned refrigerant compressor, the magnitude of this couple changes with the stroke change. In such a mechanism, there is also a socket plate which by its wobbling adds to the rotating couple caused by the pistons. In arrangements such as the above-noted compressor, the location of the swash plate tilt axis is determined by mechanical considerations and it is not reasonably possible to provide counterweights sufficient to move the swash plate's mass centroid to its tilt axis for balancing as the added masses would interfere with the working mechanism. And if mass was added to the swash plate to balance the rotating couple and static unbalance at one swash plate angle, this would move the mass centroid further from the tilt axis and thereby increase the static unbalance at all other swash plate angles.